Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 14 »

*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 14 Dec 2010 13:00:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292331558x8moptex9fh1x9j.htm/, Retrieved Tue, 14 Dec 2010 13:59:20 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/14/t1292331558x8moptex9fh1x9j.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 301631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224 275902 271115 277509 279681

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.8889	6.9425	0
2	0.709946	5.5449	0
3	0.590474	4.6117	1e-05
4	0.556337	4.3451	2.7e-05
5	0.573054	4.4757	1.7e-05
6	0.576368	4.5016	1.5e-05
7	0.516025	4.0303	7.9e-05
8	0.435579	3.402	0.000593
9	0.394294	3.0795	0.001553
10	0.427192	3.3365	0.000724
11	0.510906	3.9903	9e-05
12	0.532144	4.1562	5.1e-05
13	0.396682	3.0982	0.001471
14	0.215166	1.6805	0.048987
15	0.092378	0.7215	0.23668
16	0.041718	0.3258	0.372835
17	0.03481	0.2719	0.393319
18	0.019782	0.1545	0.438863
19	-0.048334	-0.3775	0.353557
20	-0.135231	-1.0562	0.147524
21	-0.184272	-1.4392	0.077601
22	-0.165456	-1.2923	0.100572
23	-0.105778	-0.8262	0.205968
24	-0.090266	-0.705	0.241747
25	-0.185637	-1.4499	0.076109
26	-0.304645	-2.3793	0.010243
27	-0.368911	-2.8813	0.00273
28	-0.376922	-2.9439	0.00229
29	-0.348851	-2.7246	0.004194
30	-0.326407	-2.5493	0.006662
31	-0.349548	-2.7301	0.004133
32	-0.389623	-3.0431	0.001726
33	-0.391339	-3.0565	0.001661
34	-0.34925	-2.7277	0.004159
35	-0.284877	-2.225	0.014896
36	-0.255016	-1.9917	0.025441
37	-0.290631	-2.2699	0.01338
38	-0.338812	-2.6462	0.00517
39	-0.349887	-2.7327	0.004103
40	-0.322077	-2.5155	0.007268
41	-0.265615	-2.0745	0.021129
42	-0.220013	-1.7184	0.045402
43	-0.209095	-1.6331	0.053802
44	-0.214583	-1.6759	0.049434
45	-0.201204	-1.5715	0.060625
46	-0.165964	-1.2962	0.099892
47	-0.120273	-0.9394	0.175625
48	-0.092245	-0.7205	0.236999
49	-0.097434	-0.761	0.224799
50	-0.110562	-0.8635	0.195618
51	-0.106289	-0.8301	0.204846
52	-0.08122	-0.6344	0.264112
53	-0.041738	-0.326	0.372776
54	-0.01378	-0.1076	0.457322
55	-0.012882	-0.1006	0.460094
56	-0.025509	-0.1992	0.421371
57	-0.029161	-0.2278	0.4103
58	-0.023647	-0.1847	0.427042
59	-0.012907	-0.1008	0.460017
60	-0.005866	-0.0458	0.481804

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.8889	6.9425	0
2	-0.38215	-2.9847	0.00204
3	0.323269	2.5248	0.007096
4	0.148666	1.1611	0.125058
5	0.129755	1.0134	0.157432
6	-0.03709	-0.2897	0.38652
7	-0.153874	-1.2018	0.117045
8	0.104625	0.8171	0.208512
9	0.078151	0.6104	0.271939
10	0.221622	1.7309	0.04426
11	0.155715	1.2162	0.114302
12	-0.281126	-2.1957	0.015965
13	-0.537125	-4.1951	4.5e-05
14	0.076203	0.5952	0.276966
15	-0.059172	-0.4621	0.322809
16	-0.164737	-1.2866	0.101542
17	-0.079567	-0.6214	0.268313
18	-0.001644	-0.0128	0.494898
19	-0.044542	-0.3479	0.364563
20	-0.039225	-0.3064	0.380189
21	0.005498	0.0429	0.482944
22	-0.007031	-0.0549	0.478193
23	-0.033427	-0.2611	0.397459
24	0.087351	0.6822	0.248838
25	-0.029305	-0.2289	0.409864
26	0.082511	0.6444	0.260856
27	0.018104	0.1414	0.44401
28	-0.012333	-0.0963	0.46179
29	0.050669	0.3957	0.346841
30	0.01427	0.1115	0.455812
31	0.011668	0.0911	0.463843
32	0.00633	0.0494	0.480365
33	0.063403	0.4952	0.311122
34	-0.155257	-1.2126	0.114979
35	-0.032688	-0.2553	0.399675
36	0.006584	0.0514	0.479577
37	0.089209	0.6967	0.244306
38	-0.107218	-0.8374	0.202819
39	-0.065519	-0.5117	0.305348
40	0.049257	0.3847	0.350897
41	0.021081	0.1646	0.434884
42	-0.08046	-0.6284	0.266039
43	0.081638	0.6376	0.263055
44	-0.059272	-0.4629	0.322532
45	-0.105686	-0.8254	0.20617
46	-0.006805	-0.0531	0.478895
47	0.032591	0.2545	0.399967
48	0.002063	0.0161	0.493598
49	-0.005707	-0.0446	0.482297
50	0.015679	0.1225	0.451471
51	-0.022743	-0.1776	0.429803
52	-0.014897	-0.1164	0.453878
53	-0.040368	-0.3153	0.376812
54	-0.007398	-0.0578	0.477055
55	-0.069953	-0.5463	0.293409
56	-0.027838	-0.2174	0.414304
57	-0.041345	-0.3229	0.373931
58	0.023964	0.1872	0.426075
59	-0.039583	-0.3092	0.379129
60	-0.027302	-0.2132	0.415928

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292331558x8moptex9fh1x9j/16kls1292331657.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292331558x8moptex9fh1x9j/16kls1292331657.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292331558x8moptex9fh1x9j/26kls1292331657.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292331558x8moptex9fh1x9j/26kls1292331657.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

R code (references can be found in the software module):

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by